Stochastic comparisons of two finite mixtures of general family of distributions

Raju Bhakta (), Priyanka Majumder (), Suchandan Kayal () and Narayanaswamy Balakrishnan ()
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Raju Bhakta: National Institute of Technology Rourkela
Priyanka Majumder: Indian Institute of Science Education and Research Thiruvananthapuram
Suchandan Kayal: National Institute of Technology Rourkela
Narayanaswamy Balakrishnan: McMaster University

Metrika: International Journal for Theoretical and Applied Statistics, 2024, vol. 87, issue 6, No 3, 712 pages

Abstract: Abstract We consider here two finite (arithmetic) mixture models (FMMs) with general parametric family of distributions. Sufficient conditions for the usual stochastic order and hazard rate order are then established under the assumption that the model parameter vectors are connected in p-larger order, reciprocal majorization order and weak super/sub majorization order. Furthermore, we establish hazard rate order and reversed hazard rate order between two mixture random variables (MRVs) when a matrix of model parameters and mixing proportions changes to another matrix in some mathematical sense. We have also considered scale family of distributions to establish some sufficient conditions under which the MRVs have hazard rate order. Several examples are presented to illustrate and clarify all the results established here.

Keywords: FMMs; p-larger order; Reciprocally majorization order; Hazard rate order; Reversed hazard rate order; Matrix majorization; 60E15; 90B25 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00184-023-00930-4

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